Is the meter piped back to the suction side of the pump? If yes, then as per NFPA 25 you need to flow water via the test header every 3 years, so you need one. If the meter flow is to a drain or back to the tank, where you can actually flow water, then a meter is OK.
I had a flow meter only back to the suction side of the pump on a $1 billion hospital, the test header was removed as part of an addition 10 years ago. The pump tested was fine for the 10 years via the meter. As the insurance engineer I wanted a test header to flow water as per 25. They did not want to do it because of $$$, local AHJ had no problem with no water flowing. I stuck to my guns, they installed the test header. Witnessed the flow test, 1st hose header valve opens, suction pressure goes to 0psi! The curb box valve was closed in the street to the pump when they added the new addition, they were so happy I was a pain in the butt and stuck to my guns.